For each of the graphs given in Fig. select the equation whose graph it is from the choices given below :

$(a)$ For Fig. $(i)$,

$(i)$ $x+y=0$           $(ii)$ $y=2 x$            $(iii)$ $y=x$             $(iv)$ $y=2 x+1$

$(b)$ For Fig. $(ii)$,

$(i)$ $x+y=0$           $(ii)$ $y=2 x$            $(iii)$ $y=2x+4$             $(iv)$ $y=x-4$

$(c)$ For Fig. $(iii)$,

$(i)$ $x+y=0$           $(ii)$ $y=2 x$            $(iii)$ $y=2x+1$             $(iv)$ $y=2 x-4$

$(a)$ In Fig. $(i)$, the points on the line are $(-1, \,-2)$, $(0,\, 0)$, $(1,\, 2)$. By inspection, $y = 2x$ is the equation corresponding to this graph. You can find that the $y$ - coordinate in each case is double that of the $x$ - coordinate.

$(b)$ In Fig. $(ii)$, the points on the line are $(-2,\, 0)$, $(0,\, 4)$, $(1,\, 6)$. You know that the coordinates of the points of the graph (line) satisfy the equation $y = 2x + 4.$ So, $y = 2x + 4$ is the equation corresponding to the graph in Fig. $(ii)$.

$(c)$ In Fig. $(iii)$, the points on the line are $(-\,1, \,-\,6)$, $(0, \,-\,4)$, $(1, \,-\,2),$  $(2,\, 0)$. By inspection, you can see that $y = 2x -4 $ is the equation corresponding to the given graph (line).